High pressure reciprocating pump and control of the same

ABSTRACT

Pumping for chromatograph applications calls for constant flow at high pressures and for accurate control of liquid composition. A two-cylinder pump, and associated controls provide an accurate, fixed flow rate. During the initial portion of the pumping stroke of a first piston, while its check valve remains closed, a second piston provides all the flow required at a fixed rotational speed. Once the pressure inside the first piston&#39;s cylinder has reached that of the discharge and its discharge check valve opens, the control system switches to a constant-pressure control mode, to maintain a fixed flow rate. Constant-pressure control is switched off when the second piston&#39;s discharge check valve closes, and pump control returns to fixed rotational speed. Determining the angular displacement at which to effect these control-mode switches is carried out by monitoring changes in the discharge pressure.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to a method and apparatus forconfiguring and controlling a two-cylinder, reciprocating pump such thatit pumps a constant volumetric flow rate at any discharge pressure. Sucha pump is useful for applications such as chromatography, which requiresaccurate, constant flow rates from pumps at high and variable dischargepressure. More particularly the present invention utilizes a constantrotational speed for most of a given cycle, but utilizes pressurecontrol (and slightly varying rotational speed) for a portion of thecycle in which the flow would normally increase if rotational speed ismaintained a constant. As a consequence, the pressure control acts tocontrol the rotational speed to an amount very close to the previousspeed. Another advantage is a largely constant volumetric input flowrate which improves accuracy of low pressure gradient forming. A logicsystem is incorporated to provide accurate low pressure gradient formerswitching, corrected for the depressurization of each of the pumpcylinders before their refill.

2. Background Art

Pumps used for liquid chromatography have stringent requirements todeliver constant and accurate flow rates over a range of dischargepressures. Reciprocating (or piston) pumps are usually employed for thispurpose for reasons including their relatively fixed displacement.

Present-day piston pumps for chromatography are often two-cylinder pumpswhere the pistons are actuated by cams—usually one cam per piston. Thecam profiles are designed so that the sum of the positive (pumping)speeds of the pistons is a constant if the rotational speed is constant.As one piston decelerates near the end of its delivery stroke, the othercylinder has finished filling and the piston accelerates as it beginsits stroke toward the cylinder head. The result of the constant sum ofpiston velocities in this interval is, if both discharge check valvesare open, the total flow rate is constant.

When the pump discharge pressure is low (less than about 10 atmospheres,absolute), the flow rate remains constant with constant rotationalspeed. Liquids are, in fact, not truly incompressible. A measure of afluid's “compressibility” is the bulk modulus of elasticity, E_(v),defined as $E_{v} = {{{{- -}V}\frac{\mathbb{d}p}{\mathbb{d}V}} -}$where p is pressure and

is volume. The bulk modulus of elasticity is larger for a liquid than agas, but is not infinite. According to the above equation, when pressurechanges, so does the volume of a liquid. Because of this volume change,and because the components of the pump are non-rigid, the actual traveldistance from bottom dead center until the discharge check valve opensbecomes non-negligible. The result is, during this portion of the cycle,fluid is being pumped from a single cylinder only, while the shape ofthe cam profile is increasing or keeping a piston's speed constant.

Thus, at a constant rotational speed, the flow rate is less than theconstant value required. Early pumps used an accumulator to smooth thepressure and flow rate in time. In present-day pumps, the instantaneousflow deficiency is made up by increasing the rotational speed of thepump by the control system in this region.

To maintain a constant flow rate, the pump discharge pressure shouldremain constant. Present-day pumps use either a flow measurement orpressure measurement as a process variable within a high-speed controlsystem to maintain constant flow rate. The manipulated variable is thepump's rotational speed. So, during the period in which a piston istraveling toward its head while its discharge check valve is closed, thepump rotational speed must increase.

Control of the speed of the pump is based on pump discharge pressuremost of the time, despite the fact that constant speed is requiredthrough the majority of the pump's cycle. Control based on pressure issubject to the noise and response time of the sensor. In addition, theflow rate into the pump during the inflow parts of the pump cycle is notwell controlled, making it difficult to produce accurate chromatographyeluant composition gradients by repetitively and synchronously switchingeluant compositions at the pump inlet. This is referenced in the art as“low pressure gradient forming” and has the advantage that it requiresonly a single high-pressure pump, rather than the usual dual pump.

There is, therefore, a need for a pump to accurately deliver a constantflow rate fluid of controlled (gradient) composition regardless of thedischarge pressure.

SUMMARY OF THE INVENTION

A purpose of this invention is to provide a method and device capable ofproducing constant flow rates at a high discharge pressure. It hasparticular application to chromatography. To accomplish this purpose, atwo-cylinder pump is used, each piston being driven by a separate cam.Both cylinders provide constant flow at high pressure, but are placedless than the usual 180° apart over most of the rotation. For thepreferred embodiment, the delivery stroke of each piston is 240° and therefill stroke is 120°. The maximum of a refill stroke of one pistonleads the maximum of the delivery stroke of the other piston, andconversely so, by 60°. However, the fluid delivery strokes are 180°apart.

The pumped fluid has a finite bulk modulus of elasticity and thecomponents of the pump are incompletely rigid. Therefore, during aportion of the cycle of each piston, the piston is traveling toward itshead, but no fluid is being delivered. This is because the pressureinside the cylinder has not yet reached the value of the pressure in thedischarge of the pump, so the discharge check valve is closed. Thisportion of the cycle of the first piston is called recompression. Duringrecompression for one piston, the cam profile for the other piston isshaped such that the other piston is able to deliver the required flowrate. When the pressure inside the cylinder of the first piston reachesthe discharge pressure, the discharge check valve for the first pistonopens. Because the second piston is still able to supply the full flowrate, if the rotational speed remains constant, the flow rate anddischarge pressure will increase. To avoid this unwanted increase inflow rate, the pump's rotational speed must decrease.

Shortly thereafter, the second piston starts to withdraw (retract awayfrom its head), decompressing the high-pressure liquid in the chamber.When this decompression portion of the cycle is complete, the secondpiston's inlet check valve opens and inlets liquid of programmedconcentration or composition from a source at (approximately)atmospheric pressure.

Because of the varying flow rate at constant rotational speed, a controlsystem manipulating rotational speed is incorporated into the pumpsystem. During the majority of the pump's cycle, a constant rotationalspeed will result in a constant flow rate. It is only during the briefperiod, already described, when the first discharge check valve has justopened, and before a second discharge check valve closes, that therotational speed must be altered. Therefore, during most of the pump'scycle, the rotational speed is fixed. When the first piston's dischargecheck valve opens, the control system switches to pressure control todecrease the rotational speed, appropriately. Discharge pressure controlremains in effect until the discharge check valve of the second pistoncloses, at which time the pump is returned to fixed speed control.

To effect the required speed decrease, a high-speed control systemmonitors the pump discharge pressure. This discharge pressure ismeasured during the portions of the cycle in which the rotational speedis fixed and this pressure is used as a set point for the pressurecontrol system. During the portion of the cycle in which the pressurecontrol system is manipulating the rotational speed, the pressure willbe controlled to the pressure set point.

To determine what portion of the cycle in which to apply pressurecontrol, the pressure and the angular position of the cam and motorshaft are monitored continuously. The opening of a discharge check valveduring fixed-speed operation indicates the completion of recompressionand can be sensed by a pressure increase. This sudden increase inpressure is correlated to the angular position of the pump shaft, andthis opening angular-related volume displacement is stored in memory.One such opening volume displacement is stored for each of the twocylinders, comprising a first storage mode. In the same manner, when adischarge check valve closes, due to a piston having come near the endof its stroke, the discharge pressure will experience a decrease as thecam crosses over top high center. This decrease in pressure iscorrelated to the angular position of the camshaft, and this closingangular position may be stored in memory. The pressure disturbances aredetected through a high gain factor and are not usually noticeable atthe high pressure liquid outlet. One such set of opening and closingangular values are stored for each of the two cylinders. A secondsensing uses a cam or photocell detector to sense when a piston goesover bottom dead center (fully retracted).

Since each of the recompression and decompression liquid cycles are verynearly thermodynamically reversible, the decompression volume is verynearly equal to the recompression volume. As indicated above, the tworespective recompression volumes are stored in memory. These storedamounts are used respectively as decompression points to detect the endof decompression of a respective cylinder. This is necessary foraccurate synchronization of an incorporated low pressure gradientformer. By continuing to monitor the pressure, anticipatory, automaticadjustments to these stored displacements are made during operation. Anunusual cam design provides for constant fluid inlet velocity as well asconstant fluid outlet velocity with respect to constant speed of thecamshaft. Constant inlet velocity is not strictly necessary but itdecreases the cost and increases the reliability of providing highgradient accuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic of a pump.

FIG. 2 shows a control scheme.

FIG. 3 shows a plot of piston displacement versus angular displacement.

FIG. 4 shows a plot of pressure versus angular displacement.

FIG. 5 shows a pump inlet assembly, including solvent sources, valvetree, and actuation logic controller.

FIG. 6 shows a cutaway of a cylinder head with inlet and outlet ports.

FIG. 7 shows a logic diagram for low pressure gradient forming.

FIG. 8 shows the cam.

FIG. 9 shows the displacement profile of the cam with cam follower.

FIG. 10 shows the velocity profile of the cam with cam follower.

BEST MODE FOR CARRYING OUT THE INVENTION

A schematic depiction of a two-cylinder pump 100 is shown in FIG. 1.Inside the two cylinders 105 and 110, pistons 115 and 120 oscillate. Theflow entering from the sample passes through inlet check valves 125 and130 that permit the fluid to pass into the cylinder through the inletline, but disallow the fluid from exiting through the inlet line.Discharge check valves 135 and 140 function to permit the flow of fluidfrom the pump cylinders 105 and 110 but to disallow the fluid fromreentering the cylinder from the discharge line.

The velocities of the pistons 115 and 120 are dictated by cams 145 and150 that are both driven by a single shaft 155 and followers 146 and151. A variable speed electric motor 160 provides the motive power tothe slower-rotating camshaft 155 through gear box 165.

Several transmitters are shown in FIG. 1. The angular positiontransmitter 170 provides a value for the angular displacement, α, of thecamshaft 155. The angular increment transmitter 175 provides a value ofthe motor shaft's 163 incremental angular position Δθ. Shaft speed ω isequal to the first temporal derivative of θ, or the update rate of Δθthat takes place in rate converter 287. The pump discharge pressuretransmitter 180 provides a value for the pump discharge pressure, p,downstream of the discharge check valves 135 and 140. These three valuesare used by the control system to a maintain constant flow rate. Twoother transmitters 137 and 142 are optional. They are used to detect theopening of check valves 135 and 140, respectively.

A schematic of a representative control system is shown in FIG. 2. FIG.2 shows the controller using random logic to clarify operation. Asimilarly functional microprocessor could be substituted.

The transmitters 170, 175, and 180 measuring values of angulardisplacement, α, incremental angular position, Δθ, and pump dischargepressure, p, respectively, are shown once again. The pressure signal isfiltered, if necessary, in filter block 205. The filtered pressure valueis then passed on to storage block 210. Storage block 210 accepts one ormore readings outside the regions α₁≦α≦α₂ 340 and α₅≦α≦α₆ 360 (as shownin FIG. 3 and explained below). If more than one reading is taken, thevalues may be averaged to smooth out variations due to noise, etc. Theresulting value is used as the discharge pressure set point, p_(sp). Thedischarge pressure set point proceeds to pressure controller 215 whereit is actively used inside the regions α₁≦α≦α₂ 340 and α₅≦α≦α₆ 360 (FIG.3) as the pressure controller's 215 set point.

The value of the filtered pressure is also received by pressurecontroller 215 as its process variable. The error between the processvariable, p, and the set point, p_(sp) is calculated by the controllerand a rotational speed set point, ω_(sp), calculated using a controlalgorithm such as a Proportional Integral Derivative (PID) algorithm.The value of the rotational speed set point as calculated by thepressure controller is only used by the motor speed controller 230 (viathe error block 225) if α₁≦α≦α₂ or α₅≦α≦α₆ as determined by the logicblock 220. The rate converter 287 converts Δθ composition pulses fromsensor 175 on the motor shaft 163 to a signal representing the operatingspeed ω_(op) Block 225 allows the manual entry of the set point speedω_(sp) 250.

If logic block 220 determines that the angular displacement, α, isoutside the closed regions [α₁, α₂] and [α₅, α₆], an angular speed setpoint, ω_(sp), 250 is pass the error block 225, which subtracts theactual operating speed ω_(op) from ω_(sp) 250. The result of error block225 is a speed error signal ω_(e). The speed error signal is sent to themotor speed controller 230 as shown. The motor speed controller 230 usesthe error value of the angular speed, ω_(e) for maintaining the motorspeed, ω_(op), at the desired value.

A simplified depiction of the pistons' distances from their respectivebottom dead centers is shown in FIG. 3. Note that the fluid deliverytimes are twice the refill times. The duration of line 310 correspondingto inletting to the first cylinder is one half that of the line 320corresponding to the discharge of this cylinder. The same applies toline 321 and 311 for the other cylinder.

We will focus just on the piston for which the solid line is plotted inFIG. 3.

Fluid is being drawn into the cylinder through most of the piston'stravel away from the cylinder head. This portion of travel is shown asthe straight line 310. Through most of the piston's travel toward itscylinder head, fluid is being expelled to a load such as achromatograph. This portion of travel is the straight line labeled 320.At α₀ 330, the piston is at bottom dead center. Its velocity ismomentarily zero. Both its inlet and discharge check valves are closed.The piston begins its course away from bottom dead center toward α₁ 335.The process taking place when the camshaft is between the angularpositions, α₀ 330 and α₁ 335, is called “recompression:” during thisportion of the stroke, the pressure in the cylinder increases from thesuction pressure to the outlet pressure. At α₁ 335, recompression iscompleted within the corresponding cylinder and the discharge checkvalve 135 opens. Also at α₁ 335, the motor speed controller's 230 setpoint switches from a fixed value, ω_(sp), emanating from set pointblock 250 to a variable value, ω_(spp), calculated by the constantpressure controller 215. At this time, both cylinders are deliveringliquid. This mode of control (utilizing a different—approximatelyω_(op)/2—rotational speed set point, ω_(spp), from the constant pressurecontroller 215) continues through the region 340 between α₁ 335 and α₂345. Once past α₂ 345, the angular speed set point sent to the errorblock 225 reverts back to a fixed value 250, ω_(sp).

The same cycle is experienced by the other piston, having the plot ofits distance from bottom dead center versus its angular displacementdepicted by the dashed line in FIG. 3. The region in which therotational speed set point, ω_(spp), emanates from pressure controller215 is the interval 360 between α₅ 355 and α₆ 365.

To determine the angular displacement values α₁ 335 and α₂ 345 (and α₅355 and α₆ 365) at which to start and stop constant pressure control,the pressure signal is analyzed in a high-speed data analyzer thatchecks for a sudden change in the pressure signal 410 shown in FIG. 4.Without the constant pressure controller 215 of this invention, thepressure would rise as shown at 413 or 414 when both pump heads aredelivering fluid. With the pressure controller 215, during the pressurecontrolled regions 340 and 360 of the cycle, the motor slows down tokeep the pressure substantially constant is shown by the dashed lines411 and 412.

Valid values of α₁ 335 and α₂ 345 (and α₅ 355 and α₆ 365) can bedetermined, for instance, by calculating the first derivative of thesignal with respect to time, or by calculating the frequency content ofthe signal and detecting when the amplitudes of higher frequency valueschange sharply.

Another aspect of this invention is associated with the induction ofsolvent into the pump. To permit a selection of solvents to beaccurately mixed in the pump 100, a solenoid valve tree assembly 560,shown in FIG. 5, resides between the solvent source 544 and the pump100. The use of a valve tree, in which at most one of several paths canpossibly be open at a time to a plurality of solvent sources 544,simplifies switching functions, as it allows abundant time for thevalves to mechanically return after deactivation. When a flow paththrough the vale tree assembly 560 between solvent source 544 and pump100 is “open,” fluid will not flow if the pump's inlet check valves areclosed. Solvents are delivered to pump 100 during the inlet strokes 310and 321 of the pistons 115 and 120. The valve tree assembly 560 includestwo three-port valves, which are a first electrically actuated valve 540and a second electrically actuated valve 550. The solvent source 544includes three solvent sources 510, 520 and 530. If neither valve isactuated, the solvent will flow from solvent source A 510, throughvalves 540 and 550 to pump 100. When valve 550 is actuated, its port tovalve 540 is closed while its port to solvent source C 530 is open. Onlysolvent C 530 will flow in this condition. Any time it is required thateither solvent A or solvent B 510 be flowing into pump 100, valve 550must be deactuated. When valve 540 is deactuated, its port to solvent A510 is open. In order for solvent B 520 to flow into pump 100, valve 540must be actuated while valve 550 must be deactuated. In this way, any ofthe three solvents may be drawn into pump 100 while all other solventsare disallowed from flowing.

In practice, actuation of each of the valves 540 and 550 is carefullytimed within actuation logic controller 570 during the intake strokes310 of the pump's cycle such that each of the three solvents 510, 520,and 530 are accurately metered into pump 100. This is accomplished by anumber of complementary means. First is measuring the time delay of eachvalve's opening, which happens at an only roughly fixed time after thevalve is electrically activated. This delay time is electronicallystored and used to correct the activation delay time of the same valvein the following mixing cycle. This is described more fully in U.S. Pat.No. 5,158,675 assigned to Isco, Inc. and incorporated herein byreference.

Another aspect of this invention is that the inlet stroke of each pumpoccurs at a time during a period of constant displacement rate andconstant rotational speed of the associated cam 145 or 150. Thesedisplacements are those for using needle bearing style, ⅞ inch diameterroller cam followers 146 and 151 riding respectively on the cams 145 and150 (FIG. 1). The cams 145 and 150, a profile of which is shown in FIG.8, are designed such that the displacement rates are linear using thesecam followers. The actual displacement versus angular position is shownin FIG. 9. The piston velocity is, therefore, remarkably constant as canbe seen in FIG. 10. FIG. 3 shows cam and follower displacements thatcome to pointed peaks for clarity. It is more practical to use roundedpeak segments in actual mechanical systems. This does not affect theaccuracy of operation since it is based on reading and comparingpressure and cam profiles on an on-line cam angle to piston (or cam)displacement in such a way that error due to fuzzy or rounded flow ratepeaks is cancelled. This cam arrangement combined with the operationcircuit shown in FIG. 2 greatly simplifies and increases the accuracy ofthe gradient valve switching.

Calculating of completion of decompression, the time a pump cylinderstarts filling, is necessary for starting the gradient former, ifaccurate gradients are to be made (FIG. 2). Decompression is shown asthe region between α₂ 345 and α₃ 346 in FIG. 3 for one piston. The otherpiston's decompression region lies between α₆ 365 and α₇ 367. Δθ is theincremental camshaft position and is detected by Δθ photocellinterrupter 175. The rate at which Δθ changes is proportional to ω_(op),the motor shaft rotational speed operating point. The rate converter 287converts Δθ to ω_(op) and transmits it to the speed error calculationblock 225 and pressure controller 215. Δθ is also counted by thetwo-gated counters 291 and 293, which prevent gradient and gradientcycles from operating during depressurization. During recompression, thegated counter 291 counts up from α₀ 330 (cam determined) to α₁ 335(pressure determined) to determine repressurization of cylinder 1. Theup count is first divided by two in the counter 179 because the deliverystroke is twice as long as the filling stroke. The signal processing maybe compensated if necessary to match the cam peak profile, or theconverse. Then the gated counter 291 down-counts the number of Δθincrements during the depressurization time of cylinder 1 from α₆ 365 toα₇ 367 the latter of which is a count down to zero, whereupon thecounter stops. Angular position, α₀ 330, is determined from the positionof the camshaft 155. Angular position, α₁ 335, is determined by apressure increase 413. The difference between α₀ 330 and α₁ 335 equalstwice the up-count angle from α₆ 365 to α₇ 367, the decompression anglefor cylinder 1. (α₇ 367 can be calculated since α₆ 365 is determined bythe cam and the difference, α₇−α₆, can be computed from the difference,α₀−α₁.) Cylinder 2 has its recompression/decompression angle computedsimilarly by gated counter 293. The gradient former shown in FIG. 5 isactivated (refill) during operation from α₇ to α₀ for cylinder 1. Thecontrol for cylinder 2 is similar, activating the gradient former for α₃to α₄.

Values of θ may be used for the program gradient operation, butcorrected values proportional to actual displacement are better as theyare not inaccurate because of small departures of cams from ideality.For example, it is not possible to make a robust cam that produces apoint-change in slope as shown in FIG. 3 at α₂. See FIG. 10 forcomparison of results from a real cam. FIG. 7 shows the use of a lookuptable (as seen in Appendix 1) to derive very accurate displacementvalues to enable accurate gradient forming.

Referring, now, to FIG. 7, the up/down counter 705 converts Δθ pulsesfrom values from the angular increment sensor 175 to values of cam angleθ. The lookup table 710 receives values of cam angle θ from the up/downcounter 705 and outputs the corrected instantaneous cylinderdisplacement, X. However, this displacement is not corrected for thefact that flow does not begin when the piston is at bottom dead center(i.e. α₁ 335 is greater than α₀ 330). This correction may be done bysubtracting the observed values of X at the angular value, α, at whichthe discharge check valve opens and flow begins, that is, α₃ 346 and α₇367, calculated from α₁ 335 and α₅ 355 as inputted to Latch 713, whichcalculates the volume of recompression. By subtracting (in the summationblock 715) the value of the displacement when the associated dischargecheck valve opens from the instantaneous cylinder displacement, theactual volume of fluid discharged from the cylinder, Y, is determined.

The total displacement, D, corrected for decompression is calculated insummation block 717 from knowledge of the total displacement determinedfrom α₂ and α₆ 365, inputted to Latch 716; and the displacementassociated with recompression.

These corrected volumes Y and D both have the proper zero base andspread. Dividing Y by D and multiplying by 100% in division block 720produces a value equal to the instantaneous percentage of the volume, Q,delivered during a flow cycle.

The quotient, Q, is presented to a triple decision tree 725, 735, and745 along with externally set and programmed gradient set point valuesfor A %, B %, and C %. In the first decision block 725, the volumepercent, Q, is compared directly with a set point, P, for the influx ofsolvent A. If the result of decision block 725 is true, all valves willbe de-energized to permit the flow of solvent A into the pump 100.

The value of set point P is subtracted from the value, Q, in summationblock 730 to calculate a value, S, which is then compared to the setpoint, R, for solvent B. If the output of the second decision block 735is true, the valve 540 will be energized, allowing solvent B to flowinto the pump 100.

The value of S is reduced by the value of R in the summation block 740.The result is labeled U in FIG. 7. The value of U is compared withanother set point, T, in the third decision block 745. If the output ofthe third decision block 745 is true, the valve 550 will be energizedwhich allows solvent C to enter the pump 100.

Comparators 725, 735 and 745 provide control to a gradient solenoidlogic driver (not shown). Obviously, the circuit can be changed for anynumber of solenoid values and liquids by changing the decision tree.Note that, at most, only one solvent will be flowing at any instant.

If one of the cylinders does not fill completely on the refill stroke,the pressure controller 215 will accelerate the motor. As long as thepressure controller 215 does not pass α₇ 367 and α₆ 365 respectively,the control system will compensate for the cylinders not beingcompletely filled.

Still another aspect of the present invention is depicted in FIG. 6 withthe piston at top dead center. The pump cylinder head 600 (shown in theorientation it will be used) is machined to enhance the mixing of thesolvents and solutes. Specifically, the inlet port 610 is locatedfurther from the seal 615 than the outlet port 620. Mixing is enhancedwithin the space between the cylinder wall 618 and the piston 617 themixing chamber 630. In this fashion, the last solution to enter themixing chamber 630 is not the first to exit, as is the case when theseports are located directly across from one another.

Obviously many modifications and variations of the present invention arepossible in light of the above teachings. It is, therefore, to beunderstood that within the scope of the appended claims, the inventionmay be practiced otherwise than as specifically described.

1. A method for controlling a reciprocating pump comprising twocylinders with associated pistons, one discharge check valve for eachcylinder, and at least one closed interval [α₁, α₂] where α is anangular displacement; the method comprising: (a) operating thereciprocating pump at a constant angular speed except through the closedinterval [α₁, α₂]; and (b) varying a angular speed of the reciprocatingpump to maintain a constant pump discharge pressure through the closedinterval [α₁, α₂].
 2. The method of claim 1 wherein the closed interval[α₁, α₂] is defined such that, in one pump cycle: (a) α₁ is an angulardisplacement when a first cylinder's discharge check valve opens; and(b) α₂ is an angular displacement when a second cylinder's dischargecheck valve closes.
 3. The method of claim 1 wherein, in a single pumpcycle, there are two closed intervals, [α₁, α₂] and [α₃, α₄] withinwhich the angular speed of the reciprocating pump is varied to maintaina constant discharge pressure.
 4. The method of claim 1 wherein thelimits α₁ and α₂ on the closed interval [α₁, α₂] are determined by thesteps: (a) measuring the pump discharge pressure; (b) measuring theangular displacement, α, of the pump; (c) calculating a first timederivative of the pump discharge pressure; (d) storing a first value ofthe angular displacement, α₁, of the pump when the first time derivativeincreases sharply; and (e) storing a second value of the angulardisplacement, α₂, of the pump when the first time derivative againincreases sharply.
 5. The method of claim 4 wherein the pump angularspeed is held constant during the determination of α₁, and α₂.
 6. Themethod of claim 1 wherein the discharge check valves are instrumented toindicate their open and closed states and limits α₁ and α₂ on the closedinterval [α₁, α₂] are determined by the steps: (a) monitoring signalsfrom the two discharge check valves; (b) storing a first value of theangular displacement, α₁, of the pump when a first check valve opens;and (c) storing a second value of the angular displacement, α₂, of thepump when a second check valve closes.
 7. The method of claim 1including a pressure controller to calculate a variable angular speedset point, ω_(sp), at which angular speed the pump will be operated, andwherein a pressure set point for the pressure controller is a value ofpressure measured when the angular displacement, α, is not in the closedinterval, [α₁, α₂].
 8. The method of claim 1 including a pressurecontroller to calculate a variable angular speed set point, ω_(sp), atwhich angular speed the pump will be operated, and wherein a pressureset point for the pressure controller is a value of pressure measuredwhen the angular displacement, α, is not in the closed interval, [α₅,α₆].
 9. The method of claim 1 including a pressure controller tocalculate a variable angular speed set point, ω_(sp), at which angularspeed the pump will be operated, and, wherein a pressure set point forthe pressure controller is an average of a plurality of values ofpressure, all measured when the angular displacement, α, is not in theclosed interval, [α₁, α₂].
 10. The method of claim 1 including apressure controller to calculate a variable angular speed set point,ω_(sp), at which angular speed the pump will be operated, and, wherein apressure set point for the pressure controller is an average of aplurality of values of pressure, all measured when the angulardisplacement, α, is not in the closed interval, [α₅, α₆].
 11. The methodof claim 1 wherein a pumping system also includes a valve treecomprising two three-port solenoid valves operating in a cycle tomeasure three solvents into the pump, said method comprising the stepsof: (a) configuring said valves such that no more than one path betweenthe three solvents and the pump may be open at a time; (b) actuatingsaid valves within the valve tree sequentially with an associated valveactuation logic controller to time actuation of each valve tosequentially meter each of said three solvents into pump through thevalve tree; and (c) deactivating all valves simultaneously during a timein which both pump inlet check valves are closed.
 12. The method ofclaim 11 wherein each valve is sequentially activated at a timecorrected by measuring a delay time between electrical activation andfluid path transfer.
 13. The method of claim 1 wherein solvent andsolute mixing is enhanced upon induction into the pump by placement ofan inlet port and an outlet port in a mixing chamber inside a cylinderhead of the pump such that: (a) the inlet port is located toward the endfarthest from the piston; while (b) the outlet port is located closestto the piston.
 14. A method for determining a decompression volume in apump cylinder for low pressure gradient former switching, the methodcomprising the steps of: (a) determining a recompression volume for thepump cylinder; (b) determining the decompression volume as a function ofthe recompression volume; and (c) using the decompression volume to timevalve openings for low pressure gradient forming.
 15. The method ofclaim 14 wherein the recompression volume is determined by the steps of:(a) measuring an angular position of a pump camshaft; (b) recording theangular position of the pump camshaft when a discharge check valveopens; and (c) correlating the cylinder volume to the angular positionof the camshaft.
 16. The method of claim 15 wherein the opening of thedischarge check valve is detected by the steps of: (a) measuring apressure downstream of the discharge check valve; and (c) detecting whenthe pressure increased sharply.
 17. The method of claim 15 wherein theopening of the discharge check valve is detected by a sensor indicatinga state of opening of the discharge check valve.
 18. The method of claim14 wherein the function of the recompression volume states that thedecompression volume is proportional to the recompression volume. 19.The method of claim 14 wherein a duration of decompression is determinedby the steps of: (a) measuring an angular position of a pump camshaft;(b) sensing a first angular position as the angular position for which apump piston reaches top dead center; (c) utilizing the function ofrecompression to determine the decompression volume; (d) calculating asecond angular position as the angular position at which thedecompression volume is reached; and (e) detecting when the pumpcamshaft reaches said second angular position at which the decompressionvolume is reached.
 20. The method of claim 14 wherein a relationshipbetween camshaft angular position and cylinder volume is known, aduration of decompression is then determined by the steps of: (a)measuring the angular position of a pump camshaft; (b) sensing a firstangular position as the angular position, α₀, for which a pump pistonreaches bottom dead center; (c) sensing a second angular piston, α₁,when a discharge check valve opens for the pump piston; (d) calculatinga recompression volume as a function of the first and second angularpositions, α₀ and α₁; (e) utilizing the function of recompression todetermine the decompression volume; (f) sensing a third angular positionas the angular position, α₆, for which the pump piston reaches top deadcenter; (g) calculating a fourth angular position, α₇, as the angularposition at which the decompression volume is reached; and (h) detectingwhen the pump camshaft reaches said fourth angular position, α₇, atwhich the decompression volume is reached.
 21. The method of claim 20for a two-cylinder pump, the method also comprising the steps of: (a)sensing a fifth angular position as the angular position, α₄, for whicha second pump piston reaches bottom dead center; (b) sensing a sixthangular piston, α₅, when a discharge check valve opens for the secondpump piston; (c) calculating a recompression volume as a function of thefifth and sixth angular positions, α₄ and α₅; (d) utilizing the functionof recompression to determine a second decompression volume; (e) sensinga seventh angular position as the angular position, α₂, for which thesecond pump piston reaches top dead center; (f) calculating an eighthangular position, α₃, as the angular position at which the seconddecompression volume is reached; and (g) detecting when the pumpcamshaft reaches said eighth angular position, α₃, at which the seconddecompression volume is reached.
 22. An apparatus for controlling areciprocating pump comprising two cylinders with associated pistons, onedischarge check valve for each cylinder, and at least one closedinterval [α₁, α₂] where α is an angular displacement; the apparatuscomprising: (a) means for operating the reciprocating pump at a constantangular speed except through the closed interval [α₁, α₂]; and (b) meansfor varying a angular speed of the reciprocating pump to maintain aconstant pump discharge pressure through the closed interval [α₁, α₂].23. The apparatus of claim 22 wherein the closed interval [α₁, α₂] isdefined such that, in one pump cycle (a) α₁ is an angular displacementwhen a first cylinder's discharge check valve opens; and (b) α₂ is anangular displacement when a second cylinder's discharge check valvecloses.
 24. The apparatus of claim 22 wherein, in a single pump cycle,there are two closed intervals, [α₁, α₂] and [α₃, α₄] within which themeans for varying the angular speed of the reciprocating pump includesmeans for maintaining a constant discharge pressure.
 25. The apparatusof claim 22 wherein the limits α₁ and α₂ on the closed interval [α₁, α₂]are determined using: (a) a pressure sensor for measuring the pumpdischarge pressure; (b) an angular displacement sensor for measuring theangular displacement, α, of the pump; (c) means for calculating a firsttemporal derivative of the pump discharge pressure; (d) memory forstoring a first value of the angular displacement, α₁, of the pump whenthe first time derivative increases sharply; and (e) memory for storinga second value of the angular displacement, α₂, of the pump when thefirst time derivative again increases sharply.
 26. The apparatus ofclaim 25 including means for holding the pump angular speed constantduring the determination of α₁ and α₂.
 27. The apparatus of claim 22wherein the discharge check valves are supplied with sensors to indicatetheir open and closed states and limits α₁ and α₂ on the closed interval[α₁, α₂] are determined using: (a) means for monitoring signals from thetwo discharge check valves; (b) means for storing a first value of theangular displacement, α₁, of the pump when a first check valve opens;and (c) means for storing a second value of the angular displacement,α₂, of the pump when a second check valve closes.
 28. The apparatus ofclaim 22 including a pressure controller means to calculate a variableangular speed set point, ω_(sp), at which angular speed the pump will beoperated, and a pressure sensor to measure a pressure set point for thepressure controller when the angular displacement, α, is not in theclosed interval, [α₁, α₂].
 29. The apparatus of claim 28 including apressure controller means to calculate a variable angular speed setpoint, ω_(sp), at which angular speed the pump will be operated, and apressure sensor to measure a pressure set point for the pressurecontroller when the angular displacement, α, is not in a second closedinterval, [α₅, α₆] associated with a second cylinder in the pump. 30.The apparatus of claim 22 including a pressure controller to calculate avariable angular speed set point, ω_(sp), at which angular speed thepump will be operated, and including means for calculating a pressureset point for the pressure controller as an average of a plurality ofvalues of pressure, all measured when the angular displacement, α, isnot in the closed interval, [α₁, α₂].
 31. The apparatus of claim 30including a pressure controller to calculate a variable angular speedset point, ω_(sp), at which angular speed the pump will be operated, andincluding means for calculating a pressure set point for the pressurecontroller as an average of a plurality of values of pressure, allmeasured when the angular displacement, α, is not in a second closedinterval, [α₅, α₆] associated with a second cylinder in the pump. 32.The apparatus of claim 22 wherein a pumping system also includes a valvetree comprising two three-port valves to meter three solvents into thepump, said apparatus comprising: (a) configuring said valves such thatat most one path between the three solvents and the pump may be open ata time; (b) actuators for actuating said valves within the valve treesequentially with an associated valve actuation logic controller meansto time actuation of each valve to sequentially meter each of said threesolvents into pump through the valve tree; and (c) means fordeactivating all valves simultaneously during a time in which both pumpinlet check valves are closed.
 33. The apparatus of claim 32 including aclock measuring a delay time between electrical activation and fluidpath transfer wherein each valve is sequentially activated at a timecorrected by said a delay time.
 34. The apparatus of claim 22 whereinsolvent and solute mixing is enhanced upon induction into the pump byplacement of an inlet port and an outlet port in a mixing chamber insidea cylinder head of the pump such that: (a) the inlet port is locatedtoward the end farthest from the piston; while (b) the outlet port islocated closest to the piston.
 35. An apparatus for determining adecompression volume in a pump cylinder for low pressure gradient formerswitching, the apparatus comprising: (a) means for determining arecompression volume for the pump cylinder; (b) means for determiningthe decompression volume as a function of the recompression volume; and(c) means for using the decompression volume to time valve openings forlow pressure gradient forming.
 36. The apparatus of claim 35 wherein themeans for determining the recompression volume includes additionalcomponents comprising: (a) an angular position sensor for a pumpcamshaft; (b) a recorder for recording the angular position of the pumpcamshaft when a discharge check valve opens; and (c) means forcorrelating the cylinder volume to the angular position of the camshaft.37. The apparatus of claim 36 wherein the opening of the discharge checkvalve is detected using components comprising: (a) a pressure sensor formeasuring a pressure downstream of the discharge check valve; and (c) apressure-change detecting means for detecting when the pressureincreases sharply.
 38. The apparatus of claim 36 including a sensorindicating a state of opening of the discharge check valve for detectingthe opening of the discharge check valve.
 39. The apparatus of claim 35including means for calculating the function of the recompression volumeby multiplying the decompression volume by a constant factor.
 40. Theapparatus of claim 35 wherein a duration of decompression is determined,the apparatus comprising: (a) an angular position sensor for measuringan angular position of a pump camshaft; (b) means for sensing a firstangular position as the angular position for which a pump piston reachestop dead center; (c) means for utilizing the function of recompressionto determine the decompression volume; (d) means for calculating asecond angular position as the angular position at which thedecompression volume is reached; and (e) means for detecting when thepump camshaft reaches said second angular position at which thedecompression volume is reached.
 41. The apparatus of claim 35 wherein arelationship between camshaft angular position and cylinder volume isknown, a duration of decompression is then determined by the apparatuscomprising: (a) an angular position sensor for measuring the angularposition of a pump camshaft; (b) means for sensing a first angularposition as the angular position, α₀, for which a pump piston reachesbottom dead center; (c) means for sensing a second angular piston, α₁,when a discharge check valve opens for the pump piston; (d) means forcalculating a recompression volume as a function of the first and secondangular positions, α₀ and α₁; (e) means for utilizing the function ofrecompression to determine the decompression volume; (f) means forsensing a third angular position as the angular position, α₆, for whichthe pump piston reaches top dead center; (g) means for calculating afourth angular position, α₇, as the angular position at which thedecompression volume is reached; and (h) means for detecting when thepump camshaft reaches said fourth angular position, α₇, at which thedecompression volume is reached.
 42. The apparatus of claim 41 for atwo-cylinder pump, the apparatus also comprising: (a) means for sensinga fifth angular position as the angular position, α₄, for which a secondpump piston reaches bottom dead center; (b) means for sensing a sixthangular piston, α₅, when a discharge check valve opens for the secondpump piston; (c) means for calculating a recompression volume as afunction of the fifth and sixth angular positions, α₄, and α₅; (d) meansfor utilizing the function of recompression to determine a seconddecompression volume; (e) means for sensing a seventh angular positionas the angular position, α₂, for which the second pump piston reachestop dead center; (f) means for calculating an eighth angular position,α₃, as the angular position at which the second decompression volume isreached; and (g) means for detecting when the pump camshaft reaches saideighth angular position, α₃, at which the second decompression volume isreached.